T-test og variansanalyse i SAS. T-test og variansanalyse i SAS p.1/18

Transcription

1 T-test og variansanalyse i SAS T-test og variansanalyse i SAS p.1/18

2 T-test og variansanalyse i SAS T-test (Etstik, tostik, parrede observationer) Variansanalyse SAS-procedurer: PROC TTEST PROC GLM T-test og variansanalyse i SAS p.2/18

3 T-test, etstik Længde af retssager i dage: DATA time; INPUT DATALINES; ; Middelværdi på 80? PROC TTEST DATA=time H0=80; VAR time; T-test og variansanalyse i SAS p.3/18

4 T-test, etstik, output The TTEST Procedure Statistics Lower CL Upper CL Lower CL Variable N Mean Mean Mean Std Dev Std Dev time Statistics Upper CL Variable Std Dev Std Err Minimum Maximum time T-Tests Variable DF t Value Pr > t time T-test og variansanalyse i SAS p.4/18

5 T-test, tostik Golf score for mænd og kvinder: DATA scores; INPUT koen $ DATALINES; f 75 f 76 f 80 f 77 f 80 f 77 f 73 m 82 m 80 m 85 m 85 m 78 m 87 m 82 ; Samme middelværdi? PROC TTEST DATA=scores; CLASS koen; VAR score; T-test og variansanalyse i SAS p.5/18

6 T-test, tostik, output (1) The TTEST Procedure Statistics Lower CL Upper CL Lower CL Variable koen N Mean Mean Mean Std Dev Std Dev score f score m score Diff (1-2) Statistics Upper CL Variable koen Std Dev Std Err Minimum Maximum score f score m score Diff (1-2) T-test og variansanalyse i SAS p.6/18

7 T-test, tostik, output (2) T-Tests Variable Method Variances DF t Value Pr > t score Pooled Equal score Satterthwaite Unequal Equality of Variances Variable Method Num DF Den DF F Value Pr > F score Folded F T-test og variansanalyse i SAS p.7/18

8 Parret T-test Systolic Blood Pressure før og efter behandling: DATA pressure; INPUT SBPbefore SBPafter DATALINES; ; Samme middelværdi før og efter behandling? PROC TTEST DATA=pressure; PAIRED SBPbefore*SBPafter; T-test og variansanalyse i SAS p.8/18

9 Parret T-test, output The TTEST Procedure Statistics Lower CL Upper CL Lower CL Difference N Mean Mean Mean Std Dev SBPbefore - SBPafter Statistics Upper CL Difference Std Dev Std Dev Std Err Minimum Maximum SBPbefore - SBPafter T-Tests Difference DF t Value Pr > t SBPbefore - SBPafter T-test og variansanalyse i SAS p.9/18

10 PROC TTEST, syntax PROC TTEST DATA=data H0=0 ALPHA=0.05; VAR a; /* Kun en- og tostik*/ CLASS b; /* Kun tostik */ PAIRED c*d; /* Kun parret */ FREQ e; BY f; /* Kræver data sorteret efter f */ T-test og variansanalyse i SAS p.10/18

11 Variansanalyse Data Data (72 observationer): Drug, niveauer 1-4. Disease, niveauer 1-3. Respons y (med manglende værdier). PROC GLM DATA=Data; CLASS Drug Disease; MODEL y = Drug Disease Drug*Disease / SOLUTION; Alternativt: MODEL y=drug Disease MODEL y=drug*disease el. T-test og variansanalyse i SAS p.11/18

12 Variansanalyse, output (1) The GLM Procedure Class Level Information Class Levels Values drug disease Number of observations 72 NOTE: Due to missing values, only 58 observations can be used in this analysis. Dependent Variable: y Sum of Source DF Squares Mean Square F Value Pr > F Model Error Corrected Total T-test og variansanalyse i SAS p.12/18

13 Variansanalyse, output (2) R-Square Coeff Var Root MSE y Mean Source DF Type I SS Mean Square F Value Pr > F drug <.0001 disease drug*disease Source DF Type III SS Mean Square F Value Pr > F drug <.0001 disease drug*disease T-test og variansanalyse i SAS p.13/18

14 Variansanalyse, output (2) Standard Parameter Estimate Error t Value Pr > t Intercept B drug B drug B drug B drug B... disease B disease B disease B... drug*disease B drug*disease B drug*disease B... drug*disease B drug*disease B drug*disease B... drug*disease B drug*disease B drug*disease B... drug*disease B... drug*disease B... drug*disease B. T-test. og variansanalyse i. SAS p.14/18

15 Variansanalyse, output (3) The GLM Procedure Dependent Variable: y NOTE: The X X matrix has been found to be singular, and a generalized inverse was used to solve the normal equations. Terms whose estimates are followed by the letter B are not uniquely estimable. T-test og variansanalyse i SAS p.15/18

16 Test for ens varianser NB: Kun ensidet variansanalyse! Definer evt. selv produktfaktoren i SAS-datasættet. PROC GLM DATA=Data; CLASS Drug; MODEL y=drug; MEANS Drug / HOVTEST=LEVENE; T-test og variansanalyse i SAS p.16/18

17 Test for ens varianser, output Første del af output er ikke medtaget. Levene s Test for Homogeneity of y Variance ANOVA of Squared Deviations from Group Means Sum of Mean Source DF Squares Square F Value Pr > F drug Error Level of y drug N Mean Std Dev T-test og variansanalyse i SAS p.17/18

18 Varians-/kovariansanalyse, syntax PROC GLM DATA=data; CLASS a b; FREQ w; MODEL a b c d*a / SS1 SS2 SS3 SS4 SOLUTION NOINT; BY e; /* Kræver data sorteret efter e */ OUTPUT OUT=diagnostics P=predicted R=residual STUDENT=st_res; MEANS a / HOVTEST=LEVENE; /* Kun ensidet variansanalyse */ T-test og variansanalyse i SAS p.18/18